PSI - Issue 12

Enrico Armentani et al. / Procedia Structural Integrity 12 (2018) 457–470 Author name / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 12. (a) Sub-model with β = 5°; (b) Sub-model with β = 18°; (c) Sub-model with β = 30°.

For the sub-model, therefore, a more dense and more accurate mesh has been created, in particular the portion relative to the toothing and in correspondence of the connecting radius of the tooth space (Fig. 13). Displacements calculated on the cut boundary of the coarse model have been imposed as boundary conditions for the sub-model, together with the specific external pressure.

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Fig. 13. Comparison between the mesh of a sub-model tooth (a) and of the whole die (b).

5. Results analyses Analyses have been conducted for the three different case studies,  = 5°, 18° and 30°. Results are reported in terms of stress states and displacements, for the combined loads of shrinking and radial pressure. Fig. 14 shows Maximum Principal Stresses for the case  = 5° for the insert; the maximum tensile value (S1 = 263 MPa > 0) is modest and is present along the active tooth profile. On the contrary, in the upper and lower areas of the insert, with respect to the forming zone, compression stresses are always present. Instead, the highest compression stresses (maximum value S3 = -1531 MPa < 0) occur in correspondence of the outside fillet radius of the gear, in the lower part of the matrix. Maximum compression stresses are principally circumferential stresses. The maximum compression values are found far from the forming zone and only in the lower part of the die, due to the load asymmetry in axial direction. The forming pressure, which generates strong tensile stresses, tends to balance the compression stresses due to the shrinking that are located in the lower area far from the action of the powder pressure. Fig. 15 shows Von Mises stresses on the ring. In this case, the circumferential stresses are exclusively tensile, while the radial ones are exclusively compression.